Interference suppressing OFDM system for wireless communications

ABSTRACT

An IS-OFDM system for point-to-point wireless communications that suppresses narrow-band interference comprises an IS-OFDM transmitter and an IS-OFDM receiver, wherein a transmitted signal comprises a plurality of subcarriers, and further wherein each subcarrier contains more than one and potentially all symbols transmitted in a given frame. The IS-OFDM transmitted signal is at a data rate that is equal to the data rate of the input data stream via the use of P/S converters.

This application is a continuation of U.S. patent application Ser. No.13/102,887, filed May 6, 2011, now U.S. Pat. No. 8,358,574, and is acontinuation of Ser. No. 12/631,758, filed Dec. 4, 2009, now U.S. Pat.No. 7,940,639, which is a continuation of U.S. patent application Ser.No. 11/648,081, filed Dec. 29, 2006, now U.S. Pat. No. 7,630,290, whichis a continuation of U.S. patent application Ser. No. 09/969,795, filedOct. 4, 2001, now U.S. Pat. No. 7,158,474; which claims priority under35 USC §119(e) to U.S. provisional patent application Ser. No.60/269,860, filed on Feb. 21, 2001, all of which are herein incorporatedby reference in their entirety.

FIELD OF INVENTION

The present invention relates to an Orthogonal Frequency DivisionMultiplexed (OFDM) system and method that has the capabilities ofsuppressing narrow-band interference and combating channel impairment inwireless applications requiring high data rates. The InterferenceSuppression OFDM (IS-OFDM) system and method of the present inventionprovides point-to-point wireless links without spreading the incomingdata rate.

BACKGROUND OF THE INVENTION

Orthogonal Frequency Division Multiplexing (OFDM) has been accepted as amature technology for wireless broad-band communication links. Itsdesign as a multi-carrier system, allows the support of high data rateswhile maintaining symbol durations longer than the channel's dispersiontime. Thus, OFDM modems can have reliable high data rate transmission intime-dispersive or frequency-selective channels without the need forcomplex time-domain channel equalizers. OFDM can also provide highspectral efficiency by taking advantage of the adaptive nature of themulti-carrier modulation. Information feedback of the channel conditionsis used for allocating and adapting the modulation load for eachsub-carrier in order to maximize the channel throughput. Such a priorart concept, is effective when channel conditions vary slowly. Anotherprior art approach, provides suppression of narrow-band interferers byusing a hidden Markov model filter for detecting and estimatinginterference in the frequency domain.

Related prior art methods, used in multi-user communication, are knownas multi-user OFDM, multi-carrier or multi-tone CDMA. These methods arethe results of combining the OFDM with CDMA. The CDMA (binary) spreadingsequences are used for distinguishing and separating the usertransmissions while OFDM is used to enhance the link performance of eachtransmission in the presence of interference (from the other users) andchannel impairments. A multi-user OFDM or multi-carrier CDMA system maybe a synchronous one if its transmission is in the downlink(point-to-multipoint) or an asynchronous one if its transmission is inthe uplink. Also, a multi-user OFDM or multi-carrier CDMA system mayeither be a bandwidth expanding (spreading the spectrum) one or anon-bandwidth expanding (not spectrum-spreading) one. The non-bandwidthexpanding multi-carrier CDMA systems are based on the method oforthogonal code division multiplexing (OCDM), or multi-code CDMA(MC-CDMA) in which a serial-to-parallel converter is used to provideparallel outputs that are “spread” to the original input rate by meansof orthogonal sequences.

SUMMARY OF THE INVENTION

The present invention proposes an alternative improved method, whichmakes the OFDM system resistant to narrow-band interference and channelimpairments. In the proposed method the power of any transmitted symbolis distributed in more than one and possibly in all sub-carrierchannels. Hence, each sub-carrier “contains” more than one or allsymbols transmitted in a given frame. The different symbols in the samesub-carrier are separated and distinguished by orthogonal sequences.This is equivalent to having several OFDM systems combined in parallelwith the same frequency sub-carriers in which each parallel OFDM encodesthe same symbol in more than one (and possibly in all) of its frequencysub-carrier channels (frequency bins). Then, the parallel OFDM systemsare orthogonally separated with Hadamard sequences so that the OFDMsystems do not interfere with each other. Therefore, more than one, orpossibly all, frequency bins contain the same information. This providesredundancy in the case where one or more sub-carriers are affected bynarrow-band interferers or frequency-selective fading. For this reasonthe proposed OFDM system is called interference suppressing OFDM(IS-OFDM). The present invention has all of the advantages of the knownOFDM system and method (which is a special case of IS-OFDM) and,additionally, offers frequency diversity, which is the result ofdistributing the transmit power of each symbol into more than onefrequency bin. The IS-OFDM system and method of the present inventionalso allows the implementation of a multi-path resolution mechanismaided by the use of its orthogonal Hadamard sequences.

The IS-OFMA presented here is a point-to-point transmission method (nota multi-user one), which also does not spread its transmissionbandwidth. The IS-OFDM may also be viewed as an orthogonal code divisionmultiplexing (OCDM) system in which symbols are spread in parallel byorthogonal complex sequences. This type of IS-OFDM mathematical model ispresented below.

It is, therefore, an object of the present invention to provide apoint-to-point wireless link without spreading the incoming data rate.

It is yet another object of the present invention to maintain symbolduration longer than the channel's dispersion time.

It is a further object of the present invention to provide narrow-bandinterference suppression.

It is yet another object of the present invention to maintain theorthogonality between Hadamard sequences in a channel that isfrequency-selective and thus to average the power of each transmittedsymbol over all frequency bins.

It is a further object of the present invention to permit the resolutionof multi-paths.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is best described with reference to the detaileddescription and the following figures, where:

FIG. 1 is a functional block schematic diagram of an IS-OFDMtransmitter;

FIG. 2 depicts the IS-OFDM spreading operation;

FIG. 3 shows the IS-OFDM frequency spectrum;

FIG. 4 is an alternative embodiment of the IS-OFDM transmitter;

FIG. 5 is a functional block schematic diagram of an IS-OFDM receiver;

FIG. 6 illustrates the IS-OFDM synchronization process;

FIG. 7 shows IS-OFDM multi-path resolution;

FIG. 8 depicts the IS-OFDM transmitter for M=2<Ñ;

FIG. 9 shows the IS-OFDM receiver for M=2<Ñ;

FIG. 10 shows the average bit error probability (BER) of the ordinaryOFDM system versus the E_(b)/N₀ [dB] (N₀ is the power spectral densityof the AWGN) and the JSR as a parameter; and

FIG. 11 shows the average bit error probability (BER) of the IS-OFDMsystem versus the E_(b)/N₀ [dB] and the narrow-band interference powerto signal ratio JSR, as a parameter.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The IS-OFDM transmitter is illustrated in FIG. 1. The input data streamof rate R bits/sec, enters a serial-to-parallel (S/P) converter 105,which provides Ñ parallel data streams each with rate R/Ñ bits/sec. Atthe output of the S/P converter, a data signal x_(q)(T sec long), of aparallel stream q is spread (by spreader 107) by an orthogonal binaryHadamard code sequence w_(q)=[w_(q,0),w_(q,2), . . . , w_(q,Ñ−1)] forq=0, . . . , Ñ−1. After the spreading operation the signal rate is againR bits/sec. Assuming that x_(q) represents a complex-valued signalingpoint in a QAM constellation, i.e., x_(q)=α_(q)+jβ_(q), the spreadsignal then isX _(q,k) =x _(q) w _(q,k)=α_(q) w _(q,k) +jβ _(q) w _(q,k) for k=0, . .. , Ñ−1  (1)

The above process is called orthogonal code division multiplexing (OCDM)and provides a set of Ñ parallel data streams, which are separated fromeach other by orthogonal codes.

In the next step, each of the parallel orthogonal streams is processedas in an ordinary OFDM. That is, each of the spread signals enters a S/Pbit-buffer and encoder device 110, which provides N parallelsub-streams. The encoder creates N=2Ñ complex data points defined by,

$\begin{matrix}{Y_{qk} = \left\{ \begin{matrix}{\alpha_{q}w_{q,0}} & {{{for}\mspace{14mu} k} = 0} \\X_{q,k} & {{{{for}\mspace{14mu} k} = 1},2,\ldots\mspace{14mu},{\overset{\sim}{N} - 1}} \\{\beta_{q}w_{q,0}} & {{{for}\mspace{14mu} k} = \overset{\sim}{N}} \\X_{q,{N - k}}^{*} & {{{{for}\mspace{14mu} k} = {N + 1}},\ldots\mspace{14mu},{\overset{\sim}{N} - 1}}\end{matrix} \right.} & (2)\end{matrix}$

-   -   where (*) denotes complex conjugate and both Y_(q,0) and Y_(q,Ñ)        are real valued. The N parallel data streams are then input to        an inverse discrete Fourier Transform 115. Given the above        symmetry condition the output of the inverse discrete Fourier        Transform (idft or ifft) that follows is real-valued. The        resulting idft or ifft output samples then are,

$\begin{matrix}{{y_{qm} = {{\frac{1}{\sqrt{N}}{\sum\limits_{k = 0}^{N - 1}{Y_{q,k}{\mathbb{e}}^{j\; 2\;{\pi{({{km}/N})}}}\mspace{14mu}{for}\mspace{14mu} m}}} = 0}},1,\ldots\mspace{14mu},{N - 1}} & (3)\end{matrix}$The N parallel idft or ifft outputs each then enter a parallel-to-serial(P/S) converter 120, which also adds a guard-time or cyclic prefix toeach frame. The output P/S signal of the parallel stream-q then is givenby,

$\begin{matrix}{{{s_{q}(m)} = {{\frac{1}{\sqrt{N_{s}}}{\sum\limits_{k = 0}^{N - 1}{Y_{q,k}{\mathbb{e}}^{j\; 2\;{\pi{({{km}/N})}}}\mspace{14mu}{for}\mspace{14mu} m}}} = 0}},1,\ldots\mspace{14mu},{N - 1}} & (4)\end{matrix}$

where N_(s)=N+N_(g) and N_(g) is the number of guard-samples added tothe frame.

The IS-OFDM process described above takes place in parallel for each q,(q=0, 1, . . . , Ñ−1) and all Ñ parallel IS-OFDM data signals aresynchronized to each other in both frequency (rate) and timing (delay).That is, the Ñ parallel IS-OFDM data signals have exactly the samefrequency bins and their time-frames are in synch. The parallel IS-OFDMdata signals s_(q)(m) are then summed-up by an accumulator 125 toprovide the IS-OFDM signal s(m)=Σ_(q=0) ^(Ñ)s_(q)(m) which enters thedigital-to-analog (D/A) converter 130 to provide the transmit signals(t).

Details of the spreading process are illustrated in FIGS. 2 a and 2 b.Complex signaling point x_(q)=α_(q)+jβ_(q) has real component α_(q) andcomplex component β_(q). Both components are spread by the Hadamard codew_(q), which is a vector of [w_(q,k)]. The components are spread byspreaders 207. As shown in FIG. 2 b, the entire sequence of length T hasto “overlay” a single data symbol also of length T. The arrangement ofsub-carrier frequencies is illustrated in FIG. 3.

Now, using the assumption that the Ñ parallel processes of idft or ifftand P/S are synchronized, an equivalent arrangement of the above IS-OFDMtransmitter may be drawn. The input data stream of rate R bits/sec,enters a serial-to-parallel (S/P) converter 105, which provides Ñparallel data streams each with rate R/Ñ bits/sec. At the output of theS/P converter, a data signal x_(q) (T sec long), of a parallel stream qis spread by an orthogonal binary Hadamard sequencew_(q)=[w_(q,0),w_(q,2), . . . , w_(q,Ñ−1)] for q=0, . . . , Ñ−1. Afterthe spreading operation the signal rate is again R bits/sec. If theoutputs of the Ñ parallel S/P bit-buffers/encoders 110 are taken andsummed to provide Ñ parallel data points b_(k) shown in FIG. 4. Theparallel points b_(k) are given by,

$\begin{matrix}{b_{k} = {{\sum\limits_{q = 0}^{\overset{\dddot{}}{N} - 1}Y_{q,k}} = \left\{ \begin{matrix}{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{\alpha_{q}w_{q,o}}} & {{{for}\mspace{14mu} k} = 0} \\{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}w_{q,k}}} & {{{for} = 1},2,\ldots\mspace{14mu},{\overset{\sim}{N} - 1}} \\{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{\beta_{q}w_{q,o}}} & {{{for}\mspace{14mu} k} = \overset{\sim}{N}} \\{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}^{*}w_{q,{N - k}}}} & {{{{for}\mspace{14mu} k} = {\overset{\sim}{N} + 1}},\ldots\mspace{14mu},{N - 1}}\end{matrix} \right.}} & (5)\end{matrix}$Then, the N parallel points bk enter a single idft or ifft 415 followedby a P/S converter 420 (which adds guard-time or cyclic prefix to eachframe) the output of which is given by,

$\begin{matrix}\begin{matrix}{{s(m)} = {\frac{1}{\sqrt{N_{s}}}{\sum\limits_{k = 0}^{N - 1}{b_{k}{{\mathbb{e}}^{j\; 2\;{\pi{({{km}/N})}}}}^{\mspace{11mu}}}}}} \\{= {\frac{1}{\sqrt{N_{s}}}{\sum\limits_{k = 0}^{N - 1}{\sum\limits_{q = 0}^{\overset{\dddot{}}{N} - 1}{Y_{q,k}{\mathbb{e}}^{j\; 2\;{\pi{({{km}/N})}}}}}}}}\end{matrix} & (6)\end{matrix}$It is easily verified that s(m)=Σ_(q=1) ^(N)s_(q)(m), where s_(q)(m) isthe same as in equation (4). The signal s(m) is then input to an D/Aconverter 425.

Based on the above description, the Ñ incoming data symbols [x₀,x₂, . .. , x_(Ñ−1)], to the input of the IS-OFDM transmitter for the period ofa frame (Ñ=RT), can be arranged as illustrated by the matrix D_(Ñ)below.

$D_{\overset{\sim}{N}} = {\begin{bmatrix}x_{0} & x_{0} & \ldots & x_{0} \\x_{1} & x_{1} & \ldots & x_{1} \\\ldots & \ldots & \ldots & \ldots \\x_{\overset{\sim}{N} - 1} & x_{\overset{\sim}{N} - 1} & \ldots & x_{\overset{\sim}{N} - 1}\end{bmatrix}\begin{matrix}\left. \leftarrow w_{0} \right. \\\left. \leftarrow w_{1} \right. \\\; \\\left. \leftarrow w_{\overset{\sim}{N} - 1} \right.\end{matrix}}$ $\begin{matrix}\left. \mspace{40mu}\uparrow \right. & \left. \mspace{31mu}\uparrow \right. & \left. \mspace{85mu}\uparrow\mspace{70mu} \right. \\{\mspace{45mu} f_{0}} & {\mspace{31mu} f_{1}} & {\mspace{45mu} f_{\overset{\sim}{N} - 1}}\end{matrix}\mspace{11mu}$

-   -   Every OFDM frequency bin or sub-carrier f_(i), i=0, . . . , Ñ−1,        “contains” all data bits x₀, x₁, . . . , x_(Ñ−1), which are        distinguished from each other by the orthogonal Hadamard        sequences w_(q)=[w_(q,0),w_(q,2), . . . , w_(q,Ñ−1)], k=0, . . .        , Ñ−1. This means that the power of each data bit is distributed        or “spread” to all sub-carriers as opposed to the ordinary OFDM        in which a symbol belongs to only one sub-carrier.

Now consider the special case where the orthogonal sequences are notHadamard but having a (0,1) as, w_(q)=[w_(q,k)] where,

$w_{q,k} = \left\{ {\begin{matrix}1 & {{{for}\mspace{14mu} q} = k} \\0 & {{{for}\mspace{14mu} q} \neq k}\end{matrix}.} \right.$Then, it is easily verified that the IS-OFDM becomes the ordinary OFDM.Hence, the ordinary OFDM is a special case of the IS-OFDM, correspondingto the matrix D_(Ñ) shown below,

$D_{\overset{\sim}{N}} = {\begin{bmatrix}x_{0} & 0 & \ldots & 0 \\0 & x_{1} & \ldots & 0 \\\ldots & \ldots & \ldots & \ldots \\0 & 0 & \ldots & x_{\overset{\sim}{N} - 1}\end{bmatrix}\begin{matrix}\left. \leftarrow w_{0} \right. \\\left. \leftarrow w_{1} \right. \\\; \\\left. \leftarrow w_{\overset{\sim}{N} - 1} \right.\end{matrix}}$ $\begin{matrix}\left. \mspace{40mu}\uparrow \right. & \left. \mspace{31mu}\uparrow \right. & \left. \mspace{65mu}\uparrow\mspace{70mu} \right. \\{\mspace{45mu} f_{0}} & {\mspace{31mu} f_{1}} & {\mspace{20mu} f_{\overset{\sim}{N} - 1}}\end{matrix}\mspace{11mu}$

The IS-OFDM receiver is illustrated in FIG. 5. As shown, afterdemodulation and A/D conversion (by A/D converter 505) the receivedsignal r(m) enters a S/P converter 510, which provides N parallel datapoints z_(m) for m=0, 1, . . . , N−1. The parallel data z_(m) then entera discrete Fourier transform (DFT or FFT) 515, which provides N complexdata signal points given by,

$\begin{matrix}{{Z_{k}^{\prime} = {{\frac{1}{\sqrt{N}}{\sum\limits_{k = 0}^{N - 1}{x_{m}{\mathbb{e}}^{{- j}\; 2\;{\pi{({{km}/N})}}}\mspace{14mu}{for}\mspace{14mu} k}}} = 0}},1,\ldots\mspace{14mu},{N - 1}} & (7)\end{matrix}$

-   -   The above complex data signal points then enter a        decoder-demapper 520, which creates Ñ=N/2 parallel data points        defined by,

$\begin{matrix}{Z_{k} = \left\{ \begin{matrix}Z_{k}^{\prime} & {{{{for}\mspace{14mu} k} = 1},2,\ldots\mspace{14mu},{\overset{\sim}{N} - 1}} \\{{{Re}\left\{ Z_{0}^{\prime} \right\}} + {j\;{Im}\left\{ Z_{\overset{\sim}{N}}^{\prime} \right\}}} & {{{for}\mspace{14mu} k} = 0}\end{matrix} \right.} & (8)\end{matrix}$

-   -   The process up to this point can be the same as in a known OFDM        system. Now, Ñ parallel Z_(k) points enter a P/S converter 525,        the output (serial data stream) of which is despread (by        despreaders 530) by the Ñ Hadamard code sequences        w_(q)=[w_(q,0),w_(q,2), . . . , w_(q,Ñ−1)], in parallel for q=0,        1, . . . , Ñ−1. The despread data signals are then summed by        accumulators 535, as shown in FIG. 5, for producing accumulated        data streams, which are then parallel-to-serial (P/S) converted        by P/S converter 540 to produce a recovered data stream.    -   In order to verify the functional correctness of the IS-OFDM        system, assuming that the received signal at the output of the        A/D converter is the same as the transmitted signal, i.e.,        r(m)=s(m). The signal at the output of the DFT or FFT then is,

$\begin{matrix}{{b_{k} = {{\frac{1}{\sqrt{N}}{\sum\limits_{m = 0}^{N - 1}{s_{m}{\mathbb{e}}^{{- j}\; 2\;{\pi{({{km}/N})}}}\mspace{14mu}{for}\mspace{14mu} k}}} = 0}},1,\ldots\mspace{14mu},{N - 1}} & (9)\end{matrix}$

-   -   where, s_(m) are the signal points at the output of the S/P        converter and after the removal of the cyclic prefix. The signal        points at the output of the decoder-demapper then is

$\begin{matrix}{{a_{k} = {{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}w_{q,k}\mspace{14mu}{for}\mspace{14mu} k}} = 0}},1,\ldots\mspace{14mu},{\overset{\sim}{N} - 1}} & (10)\end{matrix}$

-   -   After the P/S converter the signal at the output of the        despreader-1 given by,

$\begin{matrix}\begin{matrix}{{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{a_{k}w_{1,k}}} = {\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{\left\lbrack {\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}w_{q,k}}} \right\rbrack w_{1,k}}}} \\{= {{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{w_{q,k}w_{1,k}}}}} = \left\{ \begin{matrix}{\overset{\sim}{N}}_{x_{1}} & {{{for}\mspace{14mu} q} = 1} \\0 & {{{for}\mspace{14mu} q} \neq 1}\end{matrix} \right.}}\end{matrix} & (11)\end{matrix}$

-   -   The above equation indicates that the signal power at the output        of the accumulator-1 is the total power of the signal x₁ in all        sub-carriers.

The synchronization of the IS-OFDM system consists of the frequency andthe time synchronization processes. As shown in FIG. 6, frequencysynchronization is obtained by extracting the information needed fromthe received analog signal either with explicit training data or fromthe structure of the IS-OFDM signal. Specifically, S/P converter 605,spreaders 607 and the balance of the OFDM transmitter 610 are coupled toform the OFDM transmission subsystem. A portion of the OFDM receiver 615and despreaders 630 along with accumulators 635 and P/S converter 640form the OFDM receiver subsystem. The synchronization subsystem forms aportion of the OFDM receiver subsystem and comprises frequencysynchronization unit 620, code synchronization unit 625 and codegenerators 648. Frequency synchronization unit 620 retrieves informationneeded to perform frequency synchronization from the portion of the OFDMsubsystem 615. Frequency synchronization unit 620 is coupled to codesynchronization unit 625, which is, in turn, coupled to code generators648 that are coupled to and provide input to despreaders 630. Codegenerators generate the orthogonal Hadamard code sequences locally atthe receiver. These orthogonal Hadamard code sequences have to besynchronized to the received analog signal in order to despread them.Such techniques, developed for ordinary OFDM systems may also be usedhere. After the frequency acquisition is accomplished, the orthogonalcode sequences are used to provide timing synchronization. Standard CDMAcode acquisition and tracking methods can be applied for this purpose.Given that the code sequence length is equal to the symbol length such aprocess can provide accurate symbol-level time-synchronizationcontinuously.

In addition, the parallel orthogonal sequences can be used formulti-path resolution. That is, in a multi-path propagation environment,paths that are delayed by one or more chips (of length T_(c)) can berecovered. The process is illustrated in FIG. 7. The multi-path processis very similar to the process described in FIG. 6, which is theaddition of frequency and time synchronization to the process describedin FIG. 5. Since there are multiple paths, however, in FIG. 7 there is aplurality of P/S converters 640, which each accept a plurality ofaccumulated data streams. The P/S converters 640 each produce a P/Srecovered data stream representing one of the multiple paths, where theK possible multiple paths are less than {tilde over (M)}. The P/Srecovered data streams are accepted by a maximum ratio combiner 650 toproduce a recovered data stream. The IS-OFDM code synchronizationportion of the multi-path resolution process is performed by despreaders705, which are coupled to time accumulators (integrators) 710. As shown,the set of Ñ orthogonal sequences (w₀, w₁, . . . , w_(Ñ−1)), are used toresolve up to Ñ paths. The incoming signal is frequency synchronized andDFT or FFT demodulated. Then it is despread (by despreaders 705) by codesequences w_(k) (k=0, 1, 2, . . . , Ñ−1), in parallel, where eachsequence k is delayed by kT_(c). The time accumulation for the k^(th)despreader takes place over the interval kT_(c)≦t≦T+kT_(c), whereT=ÑT_(c). The time accumulated signals produced by the time accumulatorsare then each input to a threshold circuit 715. Since each received pathcontains all Ñ codes in synchronization, the above parallel codeacquisition method can recover up to Ñ paths. The process describedabove is for a K-finger IS-OFDM rake receiver.

The IS-OFDM concept can be extended for cases where an incomingsignaling point x_(q) is assigned into only M out of Ñ frequency bins,M<Ñ. In the examples below, the cases M=2<Ñ and M=Ñ/2 are considered andillustrated by the matrices D₂ and D_(Ñ/2) respectively.

$D_{2} = {\begin{bmatrix}x_{0} & x_{0} & \ldots & x_{\overset{\sim}{N} - 2} & x_{\overset{\sim}{N} - 2} \\x_{1} & x_{1} & \ldots & x_{\overset{\sim}{N} - 1} & x_{\overset{\sim}{N} - 1}\end{bmatrix}\begin{matrix}\left. \leftarrow w_{0} \right. \\\left. \leftarrow w_{1} \right. \\\;\end{matrix}}$ $\begin{matrix}\left. \mspace{59mu}\uparrow \right. & \left. \;\uparrow\mspace{25mu} \right. & \left. \mspace{45mu}\uparrow\mspace{31mu} \right. \\{\mspace{59mu} f_{0}} & {f_{1}\mspace{14mu}} & {\mspace{31mu} f_{\overset{\sim}{N} - 2}}\end{matrix}\mspace{14mu}\begin{matrix}\left. \mspace{11mu}\uparrow\mspace{31mu} \right. \\{\mspace{11mu} f_{\overset{\sim}{N} - 1}}\end{matrix}$ $D_{\overset{\sim}{N}/2} = {\begin{bmatrix}x_{0} & \ldots & x_{0} & x_{\frac{\overset{\sim}{N}}{2}} & \ldots & x_{\frac{\overset{\sim}{N}}{2}} \\x_{1} & \ldots & x_{1} & x_{\frac{\overset{\sim}{N}}{2} + 1} & \ldots & x_{\frac{\overset{\sim}{N}}{2} + 1} \\\ldots & \ldots & \ldots & \ldots & \ldots & \ldots \\x_{\frac{\overset{\sim}{N}}{2} - 1} & \ldots & x_{\frac{\overset{\sim}{N}}{2} - 1} & x_{\overset{\sim}{N} - 1} & \ldots & x_{\overset{\sim}{N} - 1}\end{bmatrix}\begin{matrix}\left. \leftarrow w_{0} \right. \\\left. \leftarrow w_{1} \right. \\\; \\\left. \leftarrow w_{\frac{\overset{\sim}{N}}{2} - 1} \right.\end{matrix}}$ $\begin{matrix}\left. \uparrow \right. & \left. \mspace{40mu}\uparrow \right. & \left. \mspace{20mu}\uparrow\mspace{70mu} \right. \\{\mspace{79mu} f_{0}} & { f_{\frac{\overset{\sim}{N}}{2} - 1}} & f_{{\overset{\sim}{N} - 1}\mspace{40mu}}\end{matrix}\mspace{25mu}\begin{matrix} \uparrow \\f_{\overset{\sim}{N} - 1}\end{matrix}$

In the first case where M=2 the power of each data point is distributedinto two frequency bins while in the second case where M=Ñ/2 the powerof each data point is distributed into half of the frequency bins. Thefrequency bins having the same data point may or may not be adjacent.This alternative of having M<Ñ reduces the peak-to-average amplitude ofthe signal as compared to the case where M=Ñ, however the frequencydiversity of the signal is also reduced into M out of Ñ sub-carriers.

The IS-OFDM transmitter implementation for M=2<Ñ is illustrated in FIG.8 and the corresponding receiver is illustrated in FIG. 9. S/P converter805 is coupled to spreaders 807 with each spreader spreading only bycode w₀ or W₁. Spreaders 807 are coupled to S/P buffers and encoders810. If the outputs of the Ñ parallel S/P bit-buffers/encoders 810 aretaken and summed to provide Ñ parallel data points b_(k) shown in FIG.8. Then, the N parallel points b_(k) enter a single idft or ifft 415followed by a P/S converter 420 (which adds guard-time or cyclic prefixto each frame). The signal s(m) is then input to an A/D converter 825.The transmitted signal s(m) for M<Ñ has the same expression as inequation (6) but with b_(k)=Σ_(q=0) ^(M-1)Y_(q,k).

The IS-OFDM receiver is illustrated in FIG. 9 and comprises A/Dconverter 905 coupled to S/P converter 910, which also removes thecyclic prefix. The outputs of the S/P converter 910 are input to DFT orFFT 915. The outputs of DFT or FFT 915 are input to decoder-demapper920. The A/D converter 905, S/P converter 910, DFT or FFT 915 anddecoder-demapper 920 can be considered an ordinary OFDM receiver. Thereceived signal is then processed by an ordinary OFDM receiver theoutputs of which are P/S converted by P/S converters 925 in groups of Mand despread by despreaders 930 as shown in FIG. 9 for M=2. That is, twodespreaders 930 operate on each output of each P/S converter 925. Thedespreader pair despreads the output of P/S converters 925 by usingcodes w₀ and w₁. The results of the despreaders are summed byaccumulators 935.

A simulation model was used to perform a performance evaluation.Consider b_(l,k) to be a symbol at the kth sub-carrier and the lthframe. Then, b_(k)=Σ_(q=0) ^(Ñ−1)Y_(q,k′) ^((l)), where Y_(q,k) ^((l))is the same as in equation (5). The mth idft or ifft output sample atthe ith transmitted frame is then given by,

$\begin{matrix}\begin{matrix}{{s_{l}(m)} = {\frac{1}{\sqrt{N_{s}}}{\sum\limits_{k = 0}^{{Ns} - 1}{b_{l,k}{{\mathbb{e}}^{j\; 2\;{\pi{({{km}/N})}}}}^{\mspace{11mu}}}}}} \\{= {\frac{1}{\sqrt{N_{s}}}{\sum\limits_{k = 0}^{N_{s} - 1}{\sum\limits_{q = 0}^{\overset{\dddot{}}{N} - 1}{Y_{q,k}^{(l)}{\mathbb{e}}^{j\; 2\;{\pi{({{km}/N})}}}}}}}}\end{matrix} & (12)\end{matrix}$

-   -   for m=−N_(g), . . . , N−1, There are N_(s)=N+N_(g) samples per        frame, N_(g) are the guard-samples. The equivalent time length        are T_(s)=T+T_(g), T_(g) is the guard time (or cyclic prefix),        and the sampling time interval is T_(N)=T/N.    -   The transmitted continuous time signal s(t) is given by.

$\begin{matrix}{{{s(t)} = {\frac{1}{\sqrt{T_{s}}}{\sum\limits_{l}{\sum\limits_{k}{b_{l,k}{\mathbb{e}}^{j\; 2\;\pi\;{k{({t - T_{g} - {{lT}_{s}/T}})}}}{g\left( {t - {lT}_{s}} \right)}}}}}}{{where},{{g(t)} = \left\{ {\begin{matrix}1 & {{{for}\mspace{14mu} 0} \leq t < T_{s}} \\0 & {elsewhere}\end{matrix}.} \right.}}} & (13)\end{matrix}$

First, the OFDM transmission subsystem was modeled. The wirelesscommunication channel is considered to be a multi-path fading channelhaving an impulse response h(τ;t),

$\begin{matrix}{{h\left( {\tau;t} \right)} = {\sum\limits_{i}{{h_{i}(t)}{\delta\left( {\tau - \tau_{i}} \right)}}}} & (14)\end{matrix}$

-   -   The simulation model was exercised assuming that the channel can        be modeled as wide-sense stationary process with uncorrelated        delays and further assuming that the delays τ_(i) are unchanged        during the time of interest.

Considering the autocorrelation function of the channel (or multi-pathintensity profile), +[h(τ₁;t)h*(τ₂;t+τt)]=R_(h)(τ₁;Δt)*(τ₁−τ₂), themulti-path spread (or channel dispersion) T_(m) then is the range ofvalues or τ for which R_(h)(τ;Δt)>γ_(τ)>0.

The Fourier transform of R_(h)(τ;Δt) is given by, R_(H)(Δf;Δt)=∫_(−∞)^(+∞)R_(h)(τ;Δt)e^(−j2πτΔf)dτ. The coherent bandwidth of the channel(Δf)_(c) represents the range of values or Δf for whichR_(H)(Δf)>ε_(f)>0. Then (Δf)_(c)≈1/T_(m).

For a given OFDM bandwidth B we distinguish the following two cases:

(a) If (Δf f)_(c)<<B the channel is said to be frequency-selective.

(b) (Δf)_(c)>B the channel is said to be frequency-nonselective.

In a pass-band transmission system, the transmitter time scale isunknown to the receiver. Hence, during the OFDM frame reception, thewindow setting for removal of the guard interval is usually offset by atime Δt. Similarly, the sampling time at the receiver t′_(s) cannot beidentical with the transmitter. This timing delay can be incorporatedinto a channel model represented by an equivalent impulse responseh′(τ,t)=h(τ,t−Δt)

Therefore, due to the channel dispersion described above the receivedsignal may contain disturbances caused by inter-symbol interference(ISI) and inter-(sub)channel interference (ICI). ISI and ICI may resultfrom timing offset of the frame (or symbol) being greater than the guardinterval T_(g). ISI and ICI may also result from the channel impulseresponse being longer than the guard interval T_(g).

Further considering the time variation of the channel as measured by theparameter Δt in R_(H)(Δf;Δt), the Fourier transform of R_(H)(Δf;Δt) withrespect to the variable Δt, S_(H)(Δf;λ)=∫_(−∞)^(+∞)R_(H)(Δf;Δt)e^(−jπλΔt)dΔt relates the Doppler effects to the timevariation of the channel. If Δf=0 then, S_(H)(λ)=S_(H)(Δf;λ) is thepower spectrum as a function of the Doppler frequency λ. The range ofvalues of λ for which S_(H)(λ) is essentially nonzero is theDoppler-spread B_(d) of the channel. The reciprocal of B_(d) is ameasure of the coherence time (Δt)_(c) of the channel. i.e.,(Δt)_(c)≈1/B_(d).

For a given OFDM frame or symbol length T, we distinguish the followingtwo cases:

(c) If (Δt)_(c)

T the channel is said to be time-selective.

(d) (Δt)_(c)>>T the channel is said to be time-nonselective.

-   -   The total OFDM interference in a time-selective channel (i.e.        (Δt)_(c).≦T) is dominated by the ICI while in a        time-nonselective channel ICI and ISI equally contribute to the        interference because ISI is independent of the coherence time.

In this case, consider a narrow-band interferer within the transmissionbandwidth. Assuming, however, that the timing offset is smaller than theguard interval so that no ISI or ICS occurs and further assuming thatthe channel multi-path fading is frequency-flat, i.e., Bw>(Δf)_(c). Thereceived signal is then given by,

$\begin{matrix}{{r(t)} = {{\sum\limits_{i}{{h_{i}(t)}{s\left( {t - t_{i}} \right)}}} + {I(t)} + {n(t)}}} & (15)\end{matrix}$

-   -   where, I(t) represents an interfering signal from narrow-band        transmission and n(k) is additive white Gaussian noise.

A/D converting and sampling the signal (by A/D converter 505) at timeinstants t_(n)=nT_(N)

$\begin{matrix}{{r(n)} = {{\sum\limits_{l = {- \infty}}^{+ \infty}{\sum\limits_{m = {- N_{g}}}^{N - 1}{{h_{i}(n)}{s\left( {n - m} \right)}}}} + {I(n)} + {n(n)}}} & (16)\end{matrix}$

-   -   is obtained. After S/P converting and removing the guard        interval (by S/P converter 510), the N samples received during        the lth frame (or OFDM symbol) are represented by the vector        r _(l) =[r _(l,n) ]=[r _(l,0) ,r _(l,1) , . . . , r        _(l,N−1)]  (17)

where, r_(l,n)=r((n+N_(g)+lN_(S))T).

The signal r_(l,n) will then be demodulated by the DFT or FFT 515.Assuming for the moment, that the channel remains unchanged for theduration of the OFDM frame, the output of the DFT or FFT 515 at the lthframe (or OFDM symbol) and kth sub-carrier is given by,

$\begin{matrix}{{Z_{l,k}^{\prime} = {{b_{l,k} \cdot H_{l,k}} + I_{l,k} + {\eta_{l,k}\mspace{14mu}{where}}}},{Z_{l,k}^{\prime} = {\sum\limits_{n = 1}^{N - 1}{r_{l,n}{\mathbb{e}}^{{- j}\; 2\;\pi\;{k{({n/N})}}}}}}} & (18)\end{matrix}$

-   -   where, b_(l,k) is defined in (5). H_(l,k) is the channel        transfer function (CTF) during the lth frame and at subcarrier        frequency f_(k)=k/T, which may be considered to include both the        response of the channel and the transmission filter. H_(l,k) is        given by,

$\begin{matrix}{H_{l,k} = {\sum\limits_{i}{{h_{i}(l)}{\mathbb{e}}^{{- j}\; 2\;\pi\;{k{({\tau_{i}/T})}}}}}} & (19)\end{matrix}$

-   -   Also, I_(k,l) is the DFT or FFT of I(k) and η_(k,l) is the DFT        or FFT of n_(k,l).    -   The signal Z′_(l,k) is further processed by the decoder-demapper        520, which provides the signal

$\begin{matrix}{{Z_{l,k} = {{a_{l,k} \cdot H_{l,k}} + I_{l,k} + {\eta_{l,k}\mspace{14mu}{where}}}},{a_{l,k} = {2{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}^{(l)}w_{q,k}}}}}} & (20)\end{matrix}$

-   -   for k=0, 1, . . . , Ñ−1. This signal then enters a        parallel-to-serial (P/S) converter 525, the output of which will        be despread (by despreaders 530) by each orthogonal sequence in        parallel for recovering the corresponding signaling point, and        summed by accumulators 535 as shown in FIG. 5. Now, since the        channel is a stationary process, attention may be focused on a        particular frame and the subscript l may be dropped. The output        of the despreader-1 is then given by,

1 = ⁢ ∑ k = 0 N ⃛ - 1 ⁢ Z k ⁢ w 1 , k = ⁢ ∑ k = 0 N ⃛ - 1 ⁢ a k ⁢ H k ⁢ w 1 ,k + ∑ k = 0 N ⃛ - 1 ⁢ I k ⁢ w 1 , k + ∑ k = 0 N ⃛ - 1 ⁢ η k ⁢ w 1 , k ( 21 )

-   -   Based on the assumption of frequency-flat fading, H_(k) has the        same value for all sub-channels k. Hence, H_(k)=H for k=0, 1, 2,        . . . , Ñ−1. The useful signal (represented by the first term        above) provides the signaling data point x₁ as shown below,

$\begin{matrix}\begin{matrix}{{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{a_{k}H_{k}w_{1,k}}} = {H{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{\left\lbrack {2{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}w_{q,k}}}} \right\rbrack w_{1,k}}}}} \\{= {\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}\left\lbrack {2{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q,k}w_{1,k}}}} \right\rbrack}}} \\{= \left\{ \begin{matrix}{{H\left( {2\;\overset{\sim}{N}\; x_{1}} \right)}\;} & {{{for}\mspace{14mu} q} = 1} \\0 & {{{for}\mspace{14mu} q} \neq 1}\end{matrix} \right.}\end{matrix} & (22)\end{matrix}$

-   -   Notice that in the above derivation x_(q) has the same value in        all sub-carriers k=0, 1, . . . , Ñ−1. Hence,

l = H ⁡ ( N ~ ⁢ ⁢ x 1 ) + ∑ k = 0 N ⃛ - 1 ⁢ I k ⁢ w 1 , k + ∑ k = 0 N ⃛ - 1 ⁢η k ⁢ w 1 , k ( 23 )

-   -   The total power at the output of the each despreader then is,        P_(Z)=P_(u)+P_(I)+P₀. Where P_(u) is the useful signal power and        is given by, P_(u)=N²x₁ ², (N=2Ñ). P_(I) is the interference        power and is represented as follows:        P_(I)=Var{|Σ_(k)I_(k)w_(1,k)|}=E{Σ_(k)(|I_(k)w_(1,k)|²)}.        Assuming that random variables I_(k) are independent of the        sub-carrier k, (as well as random variables w_(1,k)), then P_(I)        is given by, P_(I)=Σ_(k=1) ^(L)E[|I_(k)|²]. Also, P_(η) is the        noise power, which is given by, P_(η)=Nσ_(η) ², where σ_(η)        ²=E(η_(k) ²) for all k. The signal-to-interference and noise        ratio (SINR) then is given by,

$\begin{matrix}{{SINR} = {\frac{{\overset{\_}{P}}_{u}}{P_{I} \mp P_{\eta}} = \frac{N^{2}x_{1}^{2}}{{\sum\limits_{k = 1}^{L}{E\left\lbrack {I_{k}}^{2} \right\rbrack}} + {N\;\sigma_{\eta}^{2}}}}} & (24)\end{matrix}$

-   -   From the above equation it can be observed that the useful        signal power x₁ ² is received from all Ñ frequency bins while        the interference power only exists in L out of N frequency bins        (L<N). This is the advantage of IS-OFDM as compared with an        ordinary OFDM in which the data symbols in the frequency bins        affected by the narrow-band interference may not be recovered.        In the IS-OFDM on the other hand, the SINR is averaged over all        frequency bins since each data symbol spreads its power to all        bins.

Now considering the effects of Inter-Symbol and Inter-ChannelInterfences (ISI and ICI). ICI and ISI occurs when the channeldispersion time T_(m) (due to multi-path), is greater than the guardinterval T_(g). That is, T_(m)≧T_(g), and since T_(g)=N_(g)T_(N),T_(m)−N_(g)T_(N)

0. Then, the sampling offset Δn is, [T_(m)/T_(N)]−N_(g)≧Δn≧0. On theother hand if, T_(m).≦T_(g) or T_(m)−N_(g)T_(N)

0, no ICI or ISI will occur and any sampling offset Δn≦0 can preservethe orthogonality between consecutive symbols.

In order to demonstrate this effect first consider a single path withframe misalignment or receiver synchronization offset Δn. The receivedsignal samples may then be expressed by,

$\begin{matrix}{r_{1,n} = {{\sum\limits_{i}{{h_{i}(t)}{s\left( {n^{\prime}T_{N -}\tau_{i}} \right)}}} + {\eta\left( {n^{\prime}T_{N}} \right)}}} & (25)\end{matrix}$

-   -   where, T_(N) is the sampling interval (T_(N)=T/N),        n′=n+Δn+N_(g)+lN_(S) and the sampling offset Δn.≧0. Replacing        the transmitted signal s(t) in the above equation yields,

$\begin{matrix}{r_{1,n} = {{\sum\limits_{i}{{h_{i}(t)}\left\lbrack {\sum\limits_{l}{\sum\limits_{k}{a_{l,k}{\mathbb{e}}^{j\; 2\;\pi\;{k{\lbrack{{({{n^{1}T_{N}} - T_{g} - {lT}_{s} - \tau_{i}})}/T}\rbrack}}}{g\left( {{n^{\prime}T_{N}} - {lT}_{S} - \tau_{i}} \right)}}}} \right\rbrack}} + {n\left( {n^{\prime}T_{N}} \right)}}} & (26)\end{matrix}$

-   -   Now since Δn>0 the vector r_(l) will contain samples from both        the lth symbol the (l+1)st symbol, which will cause ICI and ISI.        That is,        r _(l) =[r _(l,Δn) ,r _(l,Δn+1) , . . . , r _(l,N−1−Δn+1) ,r        _(l+1,0) ,r _(l+1,1) , . . . , r _(l+1,Δn−1)]  (27)    -   Demodulating this vector by DFT or FFT, the output signal        z_(l,k) of a single path is given by,        z _(l,k) =u _(l,k)+(ici)_(l,k)+(isi)_(l,k)+η_(l,k)  (28)    -   where, u_(l,k) is the useful part of the signal, (ici)_(l,k) and        (isi)_(l,k) are the inter-channel and inter-symbol interferences        respectively and η_(l,k) is the DFT or FFT of the white Gaussian        noise. Each component is given below

$\begin{matrix}{u_{l,k} = {\frac{N - {\Delta\; n}}{\overset{\sim}{N}}b_{l,k}{\mathbb{e}}^{j\; 2\;\pi\;\Delta\;{n{({k/N})}}}}} & (29) \\{({ici})_{l,k} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1 - {\Delta\; n}}{\sum\limits_{{i = 1},{i \neq k}}^{N}{a_{l,i}{\mathbb{e}}^{j\; 2\;{\pi{\lbrack{{n{({i - k})}} + {{\mathbb{i}}\;\Delta\;{n/N}}}\rbrack}}}}}}}} & (30) \\{({isi})_{l,k} = {\frac{1}{N}{\sum\limits_{n = {N - {\Delta\; n}}}^{N - 1}{\sum\limits_{i = l}^{N}{a_{{l + 1},i}{\mathbb{e}}^{j\; 2\;{\pi{\lbrack{{n{({i - k})}} + {{{\mathbb{i}}{({N - \;{\Delta\; n}})}}/N}}\rbrack}}}}}}}} & (31)\end{matrix}$

Assuming now that the above offset is a result of the multi-path channelhaving a transfer function H_(l,k) for each path and further assumingthat the channel remains constant for the duration of one frame or OFDMsymbol, the signal at the output of the DFT or FFT and after thedecoder-demapper is given by,Z _(l,k) ={tilde over (H)} _(l,k) a _(l,k) e^(j2πΔn(k/N))+(ICI)_(l,k)+(ISI)_(l,k)+η_(l,k)  (32)

-   -   where, {tilde over (H)}_(l,k)=α(Δn_(i))H_(l,k) and α(Δn_(i)) is        the resulting attenuation of the symbols which is approximated        by, α(Δn_(i))=Σ_(i)|h_(i)(t)|²[(N−Δn_(i))/N].

It has been shown, that at the DFT or FFT output, and for any givenframe or OFDM symbol l, the total power of the signal P_(S)(k) (withoutthe noise) is the sum of the useful power P_(U) and the powers of theinterchannel and intersymbol interferences P_(ICI)(k) and P_(ISI)(k)respectively, i.e., P_(U)(k)+P_(ICI)(k)+P_(ISI)(k)=P_(S)(k). This meansthat, depending on the channel conditions the relative values of each ofthe three components of P_(S)(k) may vary but their sum is alwaysconstant.

As is observed in equation (32), the useful component of the signal isattenuated and rotated by a phasor with phase proportional to thesub-carrier index k and the timing offset Δn, but they are constant intime. Since the phase rotation is constant in time it will have noimpact on the system if coherent or differential modulation has beenused having a channel estimator. Then each of the N outputs of the DFTor FFT may scaled and rotated, by a channel estimator and are given by,Z _(k) =Ĥ _(k) a _(k) +I _(k)+η_(k)  (33)

-   -   In the above equation the subscript l has been dropped. Ĥ_(k) is        the estimate of sub-channel k. Also, I_(l) represents the total        inter-channel and inter-symbol interference before the        despreader.

Now, since a_(k)=2Σ_(q=0) ^(Ñ−1)x_(q) ^((l))w_(q,k) the useful datacomponent U_(l) at the output of the despreader-1 is given by,

$\begin{matrix}{U_{1} = {{\sum\limits_{k = 0}^{\overset{\sim}{N}}{{\hat{H}}_{k}a_{k}w_{1,k}}} = {N\hat{H}\; x_{1}}}} & (34)\end{matrix}$

The above equation has the same derivation as equation (22). Here againthe assumption of frequency-nonselective (frequency-flat) channel hasbeen used, that is, Ĥ_(k)≈Ĥ for all k. The normalized useful signalpower (with respect to Ĥ), then is P _(u)=P_(u)/|Ĥ|²=N²x₁ ². Theinterference noise at the output of the despreader is given by,Ī=Σ_(k=o) ^(Ñ−1)I_(k)w_(1,k).

As is known, I_(k) may be approximate to Gaussian noise with varianceVar(I_(k))=σ_(k) ². Hence, Var(Ī)=Σ_(k=o) ^(Ñ−1)w_(1,k)²Var(I_(k))=Σ_(k=o) ^(Ñ−1)2σ_(k) ².

In the above equation the assumption that the interference I_(k) isindependently distributed for each k has been made. The interferencepower at the output of the despreader then is P_(I)=2Σ_(k=o)^(Ñ−1)2σ_(k) ² and the signal to interference and noise ratio (SINR) isgiven by

$\begin{matrix}{{SINR} = {\frac{{\overset{\_}{P}}_{u}}{P_{I} \mp P_{\eta}} = \frac{N^{2}x_{1}^{2}}{{2{\sum\limits_{k = 0}^{\overset{\_}{N} - 1}\sigma_{k}^{2}}} + {N\;\sigma_{\eta}^{2}}}}} & (35)\end{matrix}$

-   -   Assuming that the interference I_(k) is also identically        distributed with variance σ₁ ²=σ_(k) ² or all k, then, SINR=Nx₁        ²/(σ₁ ²+σ_(η) ²).

As has been described above, a channel is said to be frequency-selectiveif its coherence bandwidth is much smaller than its transmissionbandwidth, i.e., (Δf)_(c)<<B. Here, in addition it can be assumed thatthe channel is time-flat (or time-nonselective) which means that thecoherence time is much greater than the frame length, i.e., (Δt)_(c)>>T.

In this case, the useful part of the signal at the output of thedespreader-1 is given by

$\begin{matrix}\begin{matrix}{U_{1} = {\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{a_{k}H_{k}w_{1,k}}}} \\{= {\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{{H_{k}\left\lbrack {\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}w_{q,k}}} \right\rbrack}w_{1,k}}}} \\{= {\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{H_{k}w_{q,k}w_{1,k}}}}}} \\{= {{x_{1}{\sum\limits_{k = 0}^{\overset{\_}{N} - 1}H_{k}}} + n_{u}}}\end{matrix} & (36)\end{matrix}$

The noise n_(u) that is introduced in this case, is due to the loss oforthogonality because the transfer function H_(k) does not have aconstant value for all k. Using the property that each row of a Hadamardmatrix in normal form (except the first one) has Ñ/2−1s and Ñ/2+1s,n_(u) is given by, n_(u)=Σ_(q=1) ^(Ñ−1)x_(q)[Σ_(m=1)^(Ñ*2−1)H_(m)−Σ_(m=Ñ/2) ^(Ñ−1)H_(m)].

For a deeply frequency-selective fading channel this noise component maybe significant. In such a case it is necessary to obtain an estimate Ĥof the transfer function of each sub-channel k (before the despreadingoperation), in order to compensate (equalize) for thefrequency-selective fading and to eliminate the “noise” n_(u). Thesignal before the despreading will then be given byZ_(k)=Ĥa_(k)+I_(k)+η_(k).

The noise power P_(I) (due to ISI and ICI, Ī=Σ_(k=0)^(Ñ−1)I_(k)w_(1,k)), at the output of the despreader then isP_(I)=2Σ_(k=o) ^(Ñ−1)σ_(k) ². In frequency-selective fading however,σ_(k) ² varies from one frequency bin k to another. Therefore, thedespreader/accumulator can maximize the signal to interference and noiseratio (SINR) by averaging over all frequency bins. Thus, the output ofthe despreader-1 is,

$\begin{matrix}{{SINR} = {\frac{P_{u}}{{E\left\{ {n_{u}}^{2} \right\}} + {2{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}\sigma_{k}^{2}}} + {N\;\sigma_{\eta}^{2}}} \approx \frac{N^{2}x_{1}^{2}{\hat{H}}^{2}}{{2{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}\sigma_{k}^{2}}} + {N\;\sigma_{\eta}^{2}}}}} & (37)\end{matrix}$

-   -   Therefore, given that the “noise” n_(u), can be eliminated, the        IS-OFDM has an advantage over the ordinary OFDM in which        frequency-selective fading may result in lost of symbols in the        frequency bins where the deep fades occur.

An OFDM channel is said to be time-selective if its coherence time issmaller than the frame or symbol length T_(s), i.e., (Δt)_(c)<T_(s). Inaddition, here it is assumed that the channel is frequency-flat (orfrequency-nonselective), which means that the coherence bandwidth isgreater than the transmission bandwidth, i.e., (Δf)_(c)>B.

Assuming that the channel impulse response is given byh(t,τ)=Σ_(i)γ_(i)(t)δ(t−τ_(i)), the received OFDM signal in time-varyingchannels is given by,

$\begin{matrix}{{r(t)} = {\sum\limits_{i}{{\gamma_{i}(t)}{s\left( {t - \tau_{i\;}} \right)}}}} & (38)\end{matrix}$

-   -   where τ_(i) is the delay of the ith path and γ_(i)(t) is its        corresponding complex amplitude. γ(t) is assumed to be a        wide-sense stationary (wss) process with zero mean, unit        variance and auto-correlation function R_(γ)(τ)=ε[γ(t+τ)γ*(t)].

The transmitted time domain signal can be represented as follows,

$\begin{matrix}{{s(t)} = {{\sum\limits_{k}{s_{k}{\mathbb{e}}^{{j2\pi}\; f_{k}t}\mspace{14mu}{for}\mspace{14mu} 0}} < t \leq T_{S}}} & (39)\end{matrix}$

-   -   where, f_(k)=f₀+kΔf is the frequency of the kth subcarrier and        Δf=1/T_(s). The received signal after the DFT or FFT        demodulation then is,

$\begin{matrix}{Z_{m}^{\prime} = {\frac{1}{T_{S}}{\int_{0}^{T_{S}}{{r(t)}\ {\mathbb{e}}^{{- {j2\pi}}\; f_{m}t}{\mathbb{d}t}}}}} & (40)\end{matrix}$

-   -   For simplicity, as is known integration has been used instead of        DFT or FFT.

Replacing r(t) and s(t) from the corresponding equations above yields,

$\begin{matrix}{Z_{m}^{\prime} = {{\sum\limits_{k}{\left\{ {\frac{1}{T_{s}}{\int_{0}^{T_{S}}{{r(t)}\ {\mathbb{e}}^{{- {j2\pi}}\;{({f_{m} - f_{k}})}t}{\mathbb{d}t}}}} \right\} s_{k}}} = {{H_{0}s_{m}} + {\sum\limits_{k \neq m}{H_{k - m}s_{k}}}}}} & (41)\end{matrix}$

-   -   where, H_(l) is defined by,

$\begin{matrix}{H_{l} = {\frac{1}{T_{s}}{\int_{0}^{T_{s}}{{\gamma(t)}\ {\mathbb{e}}^{{- {j2\pi}}\; l\;\Delta\;{ft}}{\mathbb{d}t}}}}} & (42)\end{matrix}$

-   -   H₀ represents the attenuation and phase shift of the desired        signal and H_(k)'s for k≠0 the inter-channel interference (ICI),        which is dominant in time varying channels. The above implies        that any time variation in the channel results in H_(k)≠0, for        k>0.

The signal at the output of the decoder-demapper then becomes,

$\begin{matrix}{{Z_{m} = {{H_{0}a_{m}} + {\sum\limits_{k \neq m}{H_{k - m}a_{k}}}}}{{where},{a_{m} = {2{\sum\limits_{q = 0}^{\overset{\sim}{N} - 1}{x_{q}w_{q,m}}}}}}} & (43)\end{matrix}$

-   -   After that, the signals Z_(m) are converted into serial format        and then despread in parallel by orthogonal sequences. The        output of the despreader-1 is then given by,

$\begin{matrix}{{Z_{1}—} = {{\sum\limits_{m = 0}^{\overset{\sim}{N} - 1}{Z_{m}w_{1,m}}} = {{\sum\limits_{m = 0}^{\overset{\sim}{N} - 1}{a_{m}H_{0}w_{1,m}}} + {\sum\limits_{m = 0}^{\overset{\sim}{N} - 1}{I_{m}w_{1,m}}}}}} & (44)\end{matrix}$

-   -   where, I_(m)=Σ_(k≠m)H_(m−k)a_(k) is the ICI.

The first term of the above equation is the useful part of the signal.Since H₀ is constant in the frequency domain (frequency-flat channel),the signal recovered at the output of the despreader-1 is given below,

$\begin{matrix}{{{\sum\limits_{k = 0}^{\overset{\sim}{N} - 1}{a_{k}H_{0}w_{1,k}}} = {H_{0}\left( {2\;\overset{\sim}{N}\; x_{1}} \right)}}{{where},{H_{0} = {\frac{1}{T_{S}}{\int_{0}^{T_{S}}{{\gamma(t)}\ {\mathbb{d}t}}}}}}} & (45)\end{matrix}$

-   -   The useful power then is, P_(U)=N²H₀ ²x₁ ², (N=2Ñ). The        interference power        P₁=Var{|Σ_(m)I_(m)w_(1,m)|}=E{Σ_(m)(|I_(m)w_(1,m)|²)}, assuming        that random variables I_(m) are independent, P_(I) is given by,

$\begin{matrix}{P_{I} = {{\sum\limits_{m}{E\left\lbrack {I_{m}}^{2} \right\rbrack}} = {\sum\limits_{m}\sigma_{m}^{2}}}} & (46)\end{matrix}$

-   -   As is known, σ_(m) ²=E[|I_(m)|²] is tightly bounded by,

$\begin{matrix}{{\sigma_{m}^{2} \leq {\frac{d_{1}}{12}\left( {2\pi\; f_{d}T_{S}} \right)^{2}}}\mspace{14mu}{{where},{d_{1} = {\frac{2}{f_{d}^{2}}{\int_{0}^{f_{d}}{f^{2}{S_{H}(f)}\ {\mathbb{d}f}}}}}}} & (47)\end{matrix}$

-   -   S_(H)(f) is the Fourier transform of the autocorrelation        function of γ_(i)(t), i.e., S_(H)(f)=F{R_(γ)(τ)}, and describes        the Doppler power spectrum. According to Jakes' model S_(H)(f)        is given by,

$\begin{matrix}{{S_{H}(f)} = {{\frac{1}{\pi\; f_{d}\sqrt{1 - \left( {f/f_{d}} \right)^{2}}}\mspace{14mu}{for}\mspace{14mu}{f}} \leq f_{d}}} & (48)\end{matrix}$

-   -   where, f_(d) is the Doppler frequency. The        signal-to-interference ratio then is

$\begin{matrix}{{SIR} = {\frac{P_{u}}{P_{I}} = \frac{N^{2}H_{0}^{2}x_{1}^{2}}{\sum\limits_{m = 0}^{\overset{\sim}{N} - 1}\sigma_{m}^{2}}}} & (49)\end{matrix}$

-   -   The above equation indicates that the SIR of the IS-OFDM in        time-varying channel will be better than the ordinary OFDM if        the variance σ_(m) ² varies from one frequency bin m to another.        If not, the IS and the ordinary OFDM have the same SIR        performance.

The uncoded bit error probability due to narrow-band interference andAverage White Gaussian Noise (AWGN) has been evaluated by computersimulation and comparisons between the ordinary OFDM and the IS-OFDMwireless systems.

The system parameters considered are as follows: The signal bandwidth is20 MHz and Ñ=64. The frequency sub-carriers are spaced 312 kHz apart andthe data modulation is Quad Phase Shift Keying (QPSK) for allsub-carriers. The narrow-band interference is modeled as a Gaussianprocess with constant one-sided spectral density σ_(NBI) and a totalbandwidth W_(NBI)=10 MHz. The process is the output of a 20 tap linearband-pass FIR filter, characterized by a stop-band value of −30 dB,driven at the input by a Gaussian sequence. The uncoded bit errorprobability has been evaluated for the power of interference to signalratio values JSR=−10, −8, . . . , 8, 10 dBs. JSR is defined as the ratioJSR=P_(I)/P_(S), where P_(I) is the average interference power and P_(S)is the average transmitted signal power.

FIGS. 11 and 12 show the performance results for the ordinary OFDM andIS-OFDM systems respectively. The ordinary OFDM has been generated fromthe IS-OFDM by taking an identity matrix instead of a Hadamard one, sothat the two systems are equivalent.

FIG. 10 shows the average bit error probability (BER) of the ordinaryOFDM system versus the E_(b)/N₀ [dB] (N₀ is the power spectral densityof the AWGN) and the JSR as a parameter with the values consideredabove. The performance curve for the AWGN channel is taken as abenchmark. A significant floor for BER is observed when E_(b)/N₀>10 dB.For a target BER equal to 2×10⁻², a shifting of 5 dB is visible also forlow values of JSR, e.g., JSR=−10 dB. The penalty grows dramatically forany higher value of interference power, becoming intolerable. In such acase, an Forward Error Correcting (FEC) coding of the system would notsignificantly improve the system performance.

FIG. 11 shows the average bit error probability (BER) of the IS-OFDMsystem versus the E_(b)/N₀ [dB] and the narrow-band interference powerto signal ratio JSR, as a parameter. Performance results highlight thatdegradation induced by narrow-band interference is constrained within 2dB, for JSR≦0 dB and for BER=10⁻³ instead of ∞ as in the former case.The BER can be less than 2×10⁻², even if JSR=10 dB.

The major finding showed by Monte Carlo simulations is that improvementin bit error probability due to a form of diversity introduced by theIS-OFDM system does not simply follow a proportional relation. In fact,the gain can become infinity if the target BER is fixed under the errorfloor induced by narrow-band interference.

Based on the performance evaluation and analysis presented above, theproposed IS-OFDM system can be characterized by the following features:

-   -   1. The IS-OFDM provides a point-to-point wireless link without        spreading the incoming data rate.    -   2. The IS-OFDM, as with the ordinary OFDM, is appropriate for        transmission of high data rates while maintaining symbol        duration longer than the channel's dispersion time.    -   3. The IS-OFDM provides narrow-band interference suppression.        That is, if one or more frequency bins are affected by        interference, symbols may still be recovered from the remaining        bins since each IS-OFDM symbol is transmitted in all (or at        least in two) bins.    -   4. In frequency-selective fading the IS-OFDM requires that the        transfer function of each frequency bin is equalized to a        constant value so that the orthogonality between Hadamard        sequences is maintained If this problem is solved, IS-OFDM        offers the advantage of averaging the power of each transmitted        symbol over all frequency bins (for which that symbol is        transmitted) some of which may be faded.    -   5. In time-selective fading the IS-OFDM does not have any        additional advantage, but it has all the properties of an        ordinary OFDM system.    -   6. The ordinary OFDM is a special case of the IS-OFDM in which        the Hadamard sequences (used for separating different symbols is        the same frequency bin), are replaced by non-Hadamard        (0,1)-orthogonal sequences.    -   7. The IS-OFDM system design is flexible in terms of        distributing the transmit symbol power into two, three, or all        frequency bins. When the transmit symbol power is distributed        into a smaller number of frequency bins the peak-to-average        amplitude is reduced, however the frequency diversity is also        reduced.    -   8. The IS-OFDM system allows resolution of multi-paths. Such a        mechanism, utilizes the Ñ parallel Hadamard sequences for        resolving up to Ñ paths, which are received one or more chips        apart.    -   9. Finally, the IS-OFDM may be conceived or modeled as a        multi-carrier orthogonal code division multiplexed (M-OCDM)        system utilizing complex orthogonal sequences.

In conclusion, the IS-OFDM is an innovative method for providing highbit rate in wireless transmission links, which is reliable andspectrally efficient. IS-OFDM has all the advantages of the ordinaryOFDM and additionally new ones which are the result of distributing thetransmit power of each symbol into more than one frequency bins.

It should be clear from the foregoing that the objectives of theinvention have been met. While particular embodiments of the presentinvention have been described and illustrated, it should be noted thatthe invention is not limited thereto since modifications may be made bypersons skilled in the art. The present application contemplates any andall modifications within the spirit and scope of the underlyinginvention disclosed and claimed herein.

What is claimed is:
 1. An interference suppression orthogonal frequencydivision multiplexed system, comprising: an interference suppressionorthogonal frequency division multiplexed transmitter, wherein theinterference suppression orthogonal frequency division multiplexedtransmitter comprises: a serial-to-parallel converter, theserial-to-parallel converter for accepting an input data stream and foroperating on the input data stream to produce a plurality of paralleldata streams; a plurality of spreaders, each spreader of the pluralityof spreaders coupled to the serial-to-parallel converter, each spreaderof the plurality of spreaders operates by applying an orthogonal binarycode sequence to one of the plurality of parallel data streams spreadingthe one of the plurality of parallel data streams resulting in a set ofparallel spread data streams, wherein each one of the set of parallelspread data streams comprises a plurality of sub-carriers, wherein eachone of the plurality of sub-carriers contains all data bits of the inputdata stream separated from each other by the orthogonal binary codesequence where a power of each one of the data bits is spread to all ofthe plurality of sub-carriers; and a plurality of serial-to-parallelbuffer and encoder devices, each of the plurality of serial-to-parallelbuffer and encoder devices coupled to one of the plurality of spreaders,each of the plurality of serial-to-parallel buffer and encoder devicesis for accepting one of the set of parallel spread data streams and foroperating on the one of the set of parallel spread data streams toproduce a plurality of parallel sub-streams.
 2. The interferencesuppression orthogonal frequency division multiplexed system of claim 1,further comprising: an interference suppression orthogonal frequencydivision multiplexed receiver, wherein a transmitted signal comprisesthe plurality of subcarriers, and further wherein each subcarrier of theplurality of subcarrier contains more than one symbol transmitted in agiven frame.
 3. The interference suppression orthogonal frequencydivision multiplexed system of claim 1, wherein an encoder portion ofeach of the serial-to-parallel buffer and encoder devices is further forcreating complex data points, which are used to produce the plurality ofparallel sub-streams.
 4. The interference suppression orthogonalfrequency division multiplexed system of claim 1, wherein each one ofthe plurality of parallel sub-streams is associated with a transferfunction.
 5. The interference suppression orthogonal frequency divisionmultiplexed system of claim 4, wherein the transfer function of each oneof the plurality of parallel sub-streams is equalized to a constantvalue.
 6. An interference suppression orthogonal frequency divisionmultiplexed transmitter, comprising: a serial-to-parallel converter, theserial-to-parallel converter for accepting a data stream and foroperating on the data stream to produce a plurality of parallel datastreams; a plurality of spreaders, each spreader of the plurality ofspreaders coupled to the serial-to-parallel converter, each spreader ofthe plurality of spreaders operates by applying an orthogonal binarycode sequence to one of the plurality of parallel data streams spreadingthe one of the plurality of parallel data streams resulting in a set ofparallel spread data streams, wherein each one of the set of parallelspread data streams comprises a plurality of sub-carriers, wherein eachone of the plurality of sub-carriers contains all data bits of the inputdata stream separated from each other by the orthogonal binary codesequence where a power of each one of the data bits is spread to all ofthe plurality of sub-carriers; and a plurality of serial-to-parallelbuffer and encoder devices, each of the plurality of serial-to-parallelbuffer and encoder devices coupled to one of the plurality of spreaders,each of the serial-to-parallel buffer and encoder devices is foraccepting one of the set of parallel spread data streams and foroperating on the one of the set of parallel spread data streams toproduce a plurality of parallel sub-streams.
 7. The interferencesuppression orthogonal frequency division multiplexed transmitteraccording to claim 6, wherein an encoder portion of each of theserial-to-parallel buffer and encoder devices is further for creatingcomplex data points, which are used to produce the plurality of parallelsub-streams.
 8. The interference suppression orthogonal frequencydivision multiplexed transmitter of claim 6, wherein each one of theplurality of parallel sub-streams is associated with a transferfunction.
 9. The interference suppression orthogonal frequency divisionmultiplexed transmitter of claim 8, wherein the transfer function ofeach one of the plurality of parallel sub-streams is equalized to aconstant value.
 10. An interference suppression orthogonal frequencydivision multiplexed transmitter, comprising: means forserial-to-parallel converting an input data stream to produce aplurality of parallel data streams; means for spreading each of theplurality of parallel data streams by applying an orthogonal binary codesequence resulting in a set of parallel spread data streams, whereineach one of the set of parallel spread data streams comprises aplurality of sub-carriers, wherein each one of the plurality ofsub-carriers contains all data of the input data stream separated fromeach other by the orthogonal binary code sequence such that a power ofeach one of the data bits is spread to all of the plurality ofsub-carriers; and means for serial-to-parallel buffering and encodingeach of the set of parallel data streams to produce a plurality ofparallel sub-streams.
 11. The interference suppression orthogonalfrequency division multiplexed transmitter of claim 10, wherein themeans for serial-to-parallel buffering and encoding is further forcreating complex data points, which are used to produce the plurality ofparallel sub-streams.
 12. The interference suppression orthogonalfrequency division multiplexed transmitter of claim 10, wherein each oneof the plurality of parallel sub-streams is associated with a transferfunction.
 13. The interference suppression orthogonal frequency divisionmultiplexed transmitter of claim 12, wherein the transfer function ofeach one of the plurality of parallel sub-streams is equalized to aconstant value.